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  <section id="module-sympy.physics.quantum.anticommutator">
<span id="anticommutator"></span><h1>Anticommutator<a class="headerlink" href="#module-sympy.physics.quantum.anticommutator" title="Permalink to this headline">¶</a></h1>
<p>The anti-commutator: <code class="docutils literal notranslate"><span class="pre">{A,B}</span> <span class="pre">=</span> <span class="pre">A*B</span> <span class="pre">+</span> <span class="pre">B*A</span></code>.</p>
<dl class="py class">
<dt class="sig sig-object py" id="sympy.physics.quantum.anticommutator.AntiCommutator">
<em class="property"><span class="pre">class</span> </em><span class="sig-prename descclassname"><span class="pre">sympy.physics.quantum.anticommutator.</span></span><span class="sig-name descname"><span class="pre">AntiCommutator</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">A</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">B</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/sympy/sympy/blob/00d6469eafdd4aac346a0b598184c15f2560dbe5/sympy/physics/quantum/anticommutator.py#L18-L146"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sympy.physics.quantum.anticommutator.AntiCommutator" title="Permalink to this definition">¶</a></dt>
<dd><p>The standard anticommutator, in an unevaluated state.</p>
<dl class="field-list">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>A</strong> : Expr</p>
<blockquote>
<div><p>The first argument of the anticommutator {A,B}.</p>
</div></blockquote>
<p><strong>B</strong> : Expr</p>
<blockquote>
<div><p>The second argument of the anticommutator {A,B}.</p>
</div></blockquote>
</dd>
</dl>
<p class="rubric">Explanation</p>
<p>Evaluating an anticommutator is defined <a class="reference internal" href="#r620" id="id1"><span>[R620]</span></a> as: <code class="docutils literal notranslate"><span class="pre">{A,</span> <span class="pre">B}</span> <span class="pre">=</span> <span class="pre">A*B</span> <span class="pre">+</span> <span class="pre">B*A</span></code>.
This class returns the anticommutator in an unevaluated form.  To evaluate
the anticommutator, use the <code class="docutils literal notranslate"><span class="pre">.doit()</span></code> method.</p>
<p>Canonical ordering of an anticommutator is <code class="docutils literal notranslate"><span class="pre">{A,</span> <span class="pre">B}</span></code> for <code class="docutils literal notranslate"><span class="pre">A</span> <span class="pre">&lt;</span> <span class="pre">B</span></code>. The
arguments of the anticommutator are put into canonical order using
<code class="docutils literal notranslate"><span class="pre">__cmp__</span></code>. If <code class="docutils literal notranslate"><span class="pre">B</span> <span class="pre">&lt;</span> <span class="pre">A</span></code>, then <code class="docutils literal notranslate"><span class="pre">{A,</span> <span class="pre">B}</span></code> is returned as <code class="docutils literal notranslate"><span class="pre">{B,</span> <span class="pre">A}</span></code>.</p>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">symbols</span>
<span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.physics.quantum</span> <span class="kn">import</span> <span class="n">AntiCommutator</span>
<span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.physics.quantum</span> <span class="kn">import</span> <span class="n">Operator</span><span class="p">,</span> <span class="n">Dagger</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">x</span><span class="p">,</span> <span class="n">y</span> <span class="o">=</span> <span class="n">symbols</span><span class="p">(</span><span class="s1">&#39;x,y&#39;</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">A</span> <span class="o">=</span> <span class="n">Operator</span><span class="p">(</span><span class="s1">&#39;A&#39;</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">B</span> <span class="o">=</span> <span class="n">Operator</span><span class="p">(</span><span class="s1">&#39;B&#39;</span><span class="p">)</span>
</pre></div>
</div>
<p>Create an anticommutator and use <code class="docutils literal notranslate"><span class="pre">doit()</span></code> to multiply them out.</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">ac</span> <span class="o">=</span> <span class="n">AntiCommutator</span><span class="p">(</span><span class="n">A</span><span class="p">,</span><span class="n">B</span><span class="p">);</span> <span class="n">ac</span>
<span class="go">{A,B}</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">ac</span><span class="o">.</span><span class="n">doit</span><span class="p">()</span>
<span class="go">A*B + B*A</span>
</pre></div>
</div>
<p>The commutator orders it arguments in canonical order:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">ac</span> <span class="o">=</span> <span class="n">AntiCommutator</span><span class="p">(</span><span class="n">B</span><span class="p">,</span><span class="n">A</span><span class="p">);</span> <span class="n">ac</span>
<span class="go">{A,B}</span>
</pre></div>
</div>
<p>Commutative constants are factored out:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">AntiCommutator</span><span class="p">(</span><span class="mi">3</span><span class="o">*</span><span class="n">x</span><span class="o">*</span><span class="n">A</span><span class="p">,</span><span class="n">x</span><span class="o">*</span><span class="n">y</span><span class="o">*</span><span class="n">B</span><span class="p">)</span>
<span class="go">3*x**2*y*{A,B}</span>
</pre></div>
</div>
<p>Adjoint operations applied to the anticommutator are properly applied to
the arguments:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">Dagger</span><span class="p">(</span><span class="n">AntiCommutator</span><span class="p">(</span><span class="n">A</span><span class="p">,</span><span class="n">B</span><span class="p">))</span>
<span class="go">{Dagger(A),Dagger(B)}</span>
</pre></div>
</div>
<p class="rubric">References</p>
<dl class="citation">
<dt class="label" id="r620"><span class="brackets">R620</span><span class="fn-backref">(<a href="#id1">1</a>,<a href="#id2">2</a>)</span></dt>
<dd><p><a class="reference external" href="https://en.wikipedia.org/wiki/Commutator">https://en.wikipedia.org/wiki/Commutator</a></p>
</dd>
</dl>
<dl class="py method">
<dt class="sig sig-object py" id="sympy.physics.quantum.anticommutator.AntiCommutator.doit">
<span class="sig-name descname"><span class="pre">doit</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">hints</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/sympy/sympy/blob/00d6469eafdd4aac346a0b598184c15f2560dbe5/sympy/physics/quantum/anticommutator.py#L108-L122"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sympy.physics.quantum.anticommutator.AntiCommutator.doit" title="Permalink to this definition">¶</a></dt>
<dd><p>Evaluate anticommutator</p>
</dd></dl>

</dd></dl>

</section>


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